WIGNER FUNCTION DESCRIPTION OF AC TRANSPORT THROUGH A 2-DIMENSIONAL QUANTUM POINT-CONTACT

We have calculated the admittance of a two-dimensional quantum point c ontact (QPC) using a novel variant of the Wigner distribution function (WDF) formalism. In the semiclassical approximation, a Boltzmann-like equation is derived for the partial WDF describing both propagating a nd non-propagating electron modes in an effective potential generated by the adiabatic QPC. We show that this quantum kinetic approach leads to the well known stepwise behaviour of the real part of the admittan ce (the conductance), and of the imaginary part of the admittance (the emittance), in agreement with the latest results derived by Christen and Buttiker, which is determined by the number of propagating electro n modes. It is shown that the emittance is sensitive to the geometry o f the QPC, and can be controlled by the gate voltage. We have establis hed that the emittance has contributions corresponding to both quantum inductance and quantum capacitance. Stepwise oscillations in the quan tum inductance are determined by the harmonic mean of the velocities f or the propagating modes, whereas the quantum capacitance is a signifi cant mesoscopic manifestation of the nonpropagating (reflecting) modes .